To determine the correct equation that models the wages of someone who makes [tex]$6.25 an hour, let's carefully analyze the problem and each provided option.
Given:
- \( y \) represents the total earnings in dollars.
- \( x \) represents the hours worked.
- The person makes $[/tex]6.25 an hour.
Since the person is paid [tex]$6.25 for each hour worked, the total earnings \( y \) can be calculated by multiplying the hourly wage rate by the number of hours worked \( x \).
This relationship can be expressed mathematically as:
\[ y = 6.25 \times x \]
Now let's examine each provided option:
Option A: \( x = 6.25x \)
- This equation states that the number of hours worked \( x \) is equal to 6.25 times the number of hours worked \( x \), which is incorrect because it doesn't relate the earnings to the hours worked.
Option B: \( y = 625x \)
- This equation suggests that the total earnings \( y \) are 625 times the number of hours worked \( x \). This would only be correct if the wage rate were $[/tex]625 per hour, which is not the case here.
Option C: [tex]\( x = 625y \)[/tex]
- This equation suggests that the number of hours worked [tex]\( x \)[/tex] is 625 times the total earnings [tex]\( y \)[/tex]. This reverses the relationship and also implies an incorrect wage rate.
Option D: [tex]\( y = 6.25x \)[/tex]
- This equation correctly represents the total earnings [tex]\( y \)[/tex] as 6.25 times the number of hours worked [tex]\( x \)[/tex], which matches the given hourly wage rate.
Thus, the correct equation that models the wages of someone who makes $6.25 an hour is:
Option D: [tex]\( y = 6.25x \)[/tex]
